Systolic architecture for comma-free reed-solomon decoding circuit

ABSTRACT

A Comma-Free Reed-Solomon decoding circuit based on systolic array architecture that applies to a cell search in a wideband code division multiple access system, and more particularly a decoding circuit that employs a systolic array in its circuit structure. The systolic array for the decoding circuit comprises an input pattern generator, a processing element array designed in the form of a systolic array and a boundary processing element array. Given the skewed-form output results required by the systolic array and generated by the input pattern generator, the processing element array makes a correlating comparison, and outputs the results of the correlating comparison to the boundary processing element, so as to acquire the decoding results required by the Comma-Free Reed-Solomon code. The results indicate the frame boundary and scrambling code groups of the cell search in a wideband code division multiple access system.

FIELD OF THE INVENTION

[0001] The invention generally relates to a Comma-Free Reed-Solomon decoding circuit and method that applies to cell search in the wideband code division multiple access (W-CDMA) system, and more particularly relates to a decoding circuit that employs a systolic array in its circuit structure.

BACKGROUND OF THE INVENTION

[0002] As regards the third generation partnership project (hereinafter referred as the 3GPP) wideband code division multiple access (hereinafter referred as W-CDMA) system, the cell search process employed by a cellular phone has to execute a series of detections and testing procedures of synchronization codes in order to synchronize the cellular phone with its best base station. In general, the cell search algorithm of the 3GPP W-CDMA is divided into three ordered steps, namely 1) slot synchronization, 2) frame synchronization and code-group identification, and 3) scrambling-code determination. The first step involves using a primary synchronization code (hereinafter referred as PSC) to achieve slot synchronization. The second step involves using both the secondary synchronization codes (SSCs) and the Comma-Free Reed-Solomon (hereinafter referred as CFRS) codes to achieve frame synchronization and code-group identification. The third step involves using all the possible scrambling codes of the identified code group to execute a de-scrambling procedure for scrambling-code determination. Before achieving the synchronization, the cellular phone couldn't begin to decode various channel messages broadcasted by the base station or measure various channel effects.

[0003] In this invention, we are concerned with that the second step of the synchronization procedure involves decoding the CFRS code so as to determine the frame boundary and code group. The CFRS code is a combination of Comma-Free code and Reed-Solomon code and thus it has the features of both Comma-Free code and Reed-Solomon code. The Comma-Free code has a feature that no new Comma-Free code could be created by combining any two Comma-Free codes. It is capable of both error detection and synchronization simultaneously. The synchronization capability of Comma-Free code is used by the W-CDMA to achieve frame synchronization. Generally, a Comma-Free code decoding circuit is composed of simple correlators. However, in the 3GPP W-CDMA, the Comma-Free code is transmitted intermittently as opposed to the continual transmission in other applications. Therefore, an ordinary Comma-Free code decoder is not applicable to the synchronization procedure of the 3GPP W-CDMA.

[0004] The CFRS code is also a (15, 3) Reed-Solomon (hereinafter referred as RS) code with a powerful error correction feature that is essential to the 3GPP W-CDMA. As regards the design of a RS decoder, it has been discussed in detail in many articles, and the most widely used decoding method could be summed up in four steps: 1) syndrome calculation of the received codeword, 2) error locator polynomial and error evaluator computations, 3) error location identification, and 4) error value calculation. However, in the 3GPP W-CDMA, the set of CFRS codes is composed of 64 special RS codes and thus an ordinary RS decoder is unsuitable.

[0005] The 3GPP W-CDMA uses 64 CFRS codes to represent 64 code groups. Each codeword consists of 15 symbols. Every code group includes eight scrambling codes. Every base station treats one of the eight scrambling codes of the code group to which it belongs as its scrambling code for differentiating itself from the other stations. To be connected through a certain base station, a cellular phone has to achieve scrambling code synchronization with the base station first. As described above, the synchronization process has to comprise the decoding procedure of CFRS code with a view to executing frame boundary detection and code-group determination.

[0006] The symbols of CFRS code are chosen from the elements of Galois Field (GF) (16). Among the 16 secondary synchronization codes, the n^(th) synchronization code is transmitted via a secondary synchronization channel represents that the n^(th) element of GF (16) is regarded as the code symbol. Symbols are selected to form 64 CFRS codes to represent 64 code groups, each of which consists of 15 symbols. To transmit CFRS codes, a base station sends identical codes in each frame. However, prior to frame synchronization, the initial position for the receipt of CFRS codes is not necessarily occupied by the first code symbol, but can be one of the 15 code symbols. Since the same CFRS code is transmitted in each frame, it is possible to receive 15 code symbols continuously even before a frame boundary is determined. The consecutive received 15 code symbols result in a cyclic-shift version of a CFRS codeword. The aim of decoding is to identify the received codeword is which one of the 64 CFRS codes in order to determine the code group, and to detect the cyclic-shift time cyclic-shift so as to determine the frame boundary.

[0007] According to the above description, there are 64 CFRS codes and 15 cyclic-shift versions of each codeword. Thus there can be a total of 960 (64×15) versions of cyclic-shift codeword. The determination of these 960 cyclic-shift hypotheses requires a lot of complicated calculations, and more importantly, timely accomplishment of these calculations in order to avoid delay in the synchronization procedure that may cause more serious problems. Hence, decoding speed has a direct impact on real-time synchronization. A “fast” CFRS decoder is an indispensable component for the cell search algorithm.

[0008] The decoding methods discussed in the existing literature regarding the cell search algorithm merely involve direct comparison of these 960 versions. Thus there is no better decoding method, nor is there any effective architecture for hardware implementation. Therefore, it is a good idea to use the direct decoding method based on the 960 versions to develop decoding hardware architecture that works more effectively, as well as to put forward a decoding method that is more accurate.

SUMMARY OF THE INVENTION

[0009] In view of the aforesaid technical problems, the invention provides a kind of fast decoding circuit architecture that applies to the CFRS code of the 3GPP W-CDMA, not only to support various kinds of basic cell search algorithms, but also to meet the demand for multiple decoding in multi-candidate cell search algorithms.

[0010] As regards the cell search procedure of the 3GPP W-CDMA, there are many options for the execution strategies. For example, serial execution of the three steps of the synchronization procedure, simultaneous execution of the synchronization procedure in a pipelined manner, or selecting several slot boundary candidates in step 1 and simultaneously executing steps 2 & 3 by means of the various slot boundary candidates are all possible and feasible. Each algorithm requires different CFRS decoding speed. Serial cell search does not require fast decoding. Pipelined cell search requires a decoder with high decoding speed. The multi-candidate method requires a decoder with extremely high decoding speed because of the need for frequent decoding. The invention provides the means to solve the aforesaid problems, i.e. the decoding circuits that work at high or low decoding speeds. Whenever a high decoding speed is required, it could meet the need of the cell search algorithm. Whenever a low decoding speed is acceptable, it executes decoding with the minimal number of components so as to reduce power consumption.

[0011] Another object of the invention is to provide a kind of architecture of systolic array (SA) for a CFRS decoding circuit. This kind of architecture is able to perform speedy real-time execution of decoding procedure with a view to meeting the demand for various kinds of mathematical calculations of synchronization.

[0012] To gain further insight into the characteristics and the implementation of the invention, illustrations and detailed explanations of the preferred embodiment are provided below:

BRIEF DESCRIPTION OF THE DRAWINGS

[0013]FIG. 1 depicts the comparison of the efficiency of CFRS decoding with different decoding lengths;

[0014]FIG. 2 shows a CFRS decoder based on the SA architecture, wherein x_(i) denotes the received code symbol and y_(j,i) denotes the result of a correlating comparison;

[0015]FIG. 3 depicts the structure of IPG;

[0016]FIG. 4 depicts the circuit of PE;

[0017]FIG. 5 shows the table of 64 sets of CFRS codes; and

[0018]FIG. 6 depicts the circuit of BPE.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0019] As shown in FIG. 1, the 960 versions of CFRS codes can be decoded better with a complete set of 15 code symbols rather than with part of the code symbols. Hence, in the invention, after 15 code symbols have been received, a frame boundary is determined by making reference to a direct comparison of the 15 code symbols.

[0020] In order to achieve the objects of the invention, the decoding method adopted by the SA architecture decoding circuit put forward by the invention can be denoted in the following way: $\begin{matrix} {{\left( {i,j} \right) = {{Arg}\left\{ {\max \left\{ {X_{i} \otimes H_{j}} \right\}_{j = {0 \sim 63}}^{i = {0 \sim 14}}} \right\}}}\quad,} & (1) \end{matrix}$

[0021] where i denotes the index for the 15cyclic-shift versions of X_(i),j denotes the index for the 64 CFRS codes, X_(i) denotes the result of i time(s) of rightward cyclic-shift of the received CFRS codeword, while X₀ denotes the result of arbitrary cyclic-shift of the CFRS codes received in the beginning; and, X_(up32 p55 x) ₁, x₂, x₃, . . . , x₁₅}, x_(k) ∈ GF(16), 1≦k≦15. H_(j) denotes one of the 64 CFRS codes, and H_(j={h) ₁, h₂, h₃, . . . , h₁₅}, h_(k) ∈ GF(160, 1≦k≦15. Finally, X₁ {circle over (X)} H_(j) refers to making a correlating comparison.

[0022] Explanation of the SA architecture decoding circuit put forward by the invention is provided below.

[0023] As shown in FIG. 2, the decoding circuit comprises several components, namely an Input Pattern Generator (IPG) 10, a 64×15 Processing Element Array (PEA) 20, and a 64×1 Boundary Processing Element Array (BPEA) 30.

[0024] The main function of the IPG 10 is to generate 15cyclic-shift versions from the arbitrarily cyclic-shift CFRS codes received, X, wherein X_(i), 0≦i≦14, then output these cyclic-shift versions to PEA 20 in a skewed form required by the SA architecture. The output comprises all 15 types of cyclic-shift X, and, as shown in FIG. 3, its circuit structure comprises a shift register 11, a Johnson counter 13, and a masking combinational circuit 12. Its process is described below.

[0025] First of all, a received code, X, is loaded to the shift register 11. The shift register 11 then generates its 15 versions of cyclic-shift separately. The Johnson counter 13 generates the required skewed mask. With the masking combinational circuit 12, the 15 versions cyclic-shift are turned into the required 15 cyclic-shift versions in skewed form. The skewed 15 cyclic-shift versions of X are regarded as the input to the underlying WPEA 20 that is based on SA architecture.

[0026] The PEA 20 is a kind of SA architecture composed of 64×15 PEs. The structure of each PE is shown in FIG. 4, and the primary function of the PE is to make a correlating comparison. IPG 10 generates all the 15 cyclic-shift versions that are then compared with 64 sets of CFRS codes for correlations. There are three registers in each PE, namely the H register 202, X register 201 and Y register 203. The H register 202 is for storing the code symbols, h_(k), of CFRS code beforehand, or, in other words, the 64×15 CFRS code symbols table 40 shown in FIG. 5 is put in the H register 202 of every PE of the 64×15 PEA 20 correspondingly. Since there are 64 CFRS codes, and each codeword consists of 15 code symbols, it needs to be processed by a 64×15 PEA 20. The X register 201 is for storing the code symbols, x_(k), sent by the overhead PE. Given the comparing combinational circuit 204 shown in FIG. 4, when the two code symbols stored in the X register 201 and the H register 202, respectively, are identical, an accumulator 205 accumulates the result of the correlating comparison and stores the result in the Y register 203 first. It then sends the result to the PE on its right and sends the received code symbols x_(k) to the underlying PE.

[0027] The 64×15 PEA 20 connects to a set of 64×1 BPEA 30 that lies on its right. Each row of the PEA 20 is in charge of making the correlating comparison with a CFRS codes. The last PE output of each row is the result of correlating comparison, y_(j,i). BPE compares this set of comparison results, y_(j,i) for i=0˜14. After comparing the 15 results of the same codeword, each BPE begins to compare the results of individual rows as shown in FIG. 6.

[0028] The I comparator 301 is for comparing the results of the same row. A result that is greater is stored in the maximum value and cyclic-shift index register 306 first. After the maximum result of the same row has been generated, the J comparator 302 begins to compare the maximum value of the existing row with that of the overhead row. It selects the greater one, saves it and its code group index j and cyclic-shift index i in the maximum value and group & cyclic-shift index register 308, and sends them to the underlying BPE. The multiplexer 305 makes reference to the result of the I comparator 301, and saves the greater result value, y_(j,i), and its cyclic-shift index i in the maximum value and cyclic-shift index register 306. In the event that the new y_(j,i) value is greater than the y_(j,max) value, that is, when the multiplexer 305 chooses line 1, then its cyclic-shift index i is provided by the cyclic-shift index 303. The multiplexer 307 makes reference to the result of J comparator 302, and saves the greater result value, y_(j,i), its cyclic-shift index i and code group index j, etc., in the maximum value and group & cyclic-shift index register 308. In the event that the result of the existing row, y_(j,max), is greater than the y_(j−1,max) value of the overhead row, then its group index is provided by the code group index 304.

[0029] The output of the BPE at the bottom (that is, the output result of the maximum value and group & cyclic-shift index register 308) is the result of decoding. The comparison result of the greatest correlation is the desired decoding result. The code group index j of this result denotes that the received CFRS code, X, is the j^(th) code of all the possible 64 CFRS codes, while the cyclic-shift index i denotes that the received CFRS code, X, results from i times of cyclic-shift of the original code symbol. As described in the “Background of the Invention” section of this document, in the 3GPP W-CDMA, the code group index, j, denotes a code group, while the cyclic-shift index, i, denotes a frame boundary. This is the end of step 2 of the cell search.

[0030] Please refer to FIG. 2 again. The whole decoding procedure is: load the CFRS codes received to IPG 10; the IPG 10 generates 15 versions of cyclic-shift in order; input the 15 versions of skewed-style cyclic-shift to the 64×15 PEA 20; the PEA 20 makes a correlating comparison between the 15 types of cyclic-shift and 64 sets of codes saved beforehand; a comparison is made on each row with respect to one set of possible CFRS codes; as regards the comparison result of a row, the BPE of the row identifies the most probable cyclic-shift; search vertically, that is, from the top to the bottom, and find the greatest result of cyclic-shift of individual rows; the output of the BPE at the bottom is the decoding result.

[0031] The decoding duration required by this decoding circuit is as follows: (Please refer to the aforesaid decoding process) 15 cycles after the IPG 10 has input the skewed-form cyclic-shift versions into the PEA 20, the first correlating comparison result of the first row is generated; 14 cycles later, the last correlating comparison result of the first row is generated; one cycle later, the most possible cyclic-shift version of the first row is generated and, meanwhile, the last correlating comparison result of the second row has been generated, thus the BPE of the second row only generates the most probable cyclic-shift of the second row and begins to compare the results of individual rows vertically after one more cycle. It takes 63 cycles to generate the final result. Therefore, a total of 15+14+1+1+63=94 cycles is required to finish decoding. The length of each cycle varies according to the implementation method.

[0032] From the point of view of a system, the chip rate is 3.84 MHz. In general, the minimum frequency designed by a circuit should be 3.84 MHz. In other words, the designed circuit only spends time for a maximum 94 chips on decoding. Thus, there is sufficient time to prepare for the following step of determining scrambling codes in an ordinary synchronization procedure. Even if decoding has to be executed ten or twenty times in multi-candidate cell search algorithms, this decoder is able to finish decoding before the end of the slot wherein the 15^(th) secondary synchronization code is decoded. Thus it does not delay the execution of step 3 of the cell search procedure. The total time spent: 20 (number of times of decoding)*94 (the duration of decoding)+256 (receipt of the secondary synchronization code)=2136<2560 (slot length).

[0033] While the invention has been described by way of example and in terms of a preferred embodiment, it is to be understood that the invention is not limited thereto. It should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. Therefore the scope of protection for the invention should conform to the claims attached below. 

What is claimed is:
 1. A systolic architecture for Comma-Free Reed-Solomon decoding circuit, which receives and decodes a Comma-Free Reed-Solomon (CFRS) code, comprising: an input pattern generator, which receives the arbitrarily cyclic-shift CFRS code for generating 15 cyclic-shift versions of the CFRS codes and outputs to a systolic array in a skewed style; a processing element array composed of 64×15 processing elements, for receiving skewed-form cyclic-shift CFRS codeword to make a series of correlating comparisons and output a series of correlating comparison results; and a boundary processing element array composed of 64×1 boundary processing elements, for calculating a greatest said correlating comparison result of a row of said systolic array to find greatest results of individual rows and set the acquired index as a decoding result.
 2. The systolic architecture for Comma-Free Reed-Solomon decoding circuit of claim 1, wherein said input pattern generator is composed of a shift register, a Johnson counter and a masking combinational circuit; said cyclic-shift register receives the 15 symbols of said CFRS codes, cyclically shifts them and outputs them as 15 cyclic-shift versions of said CFRS codes; said Johnson counter sends a masking signal to said masking combination circuit; said masking combination circuit outputs the skewed-form CFRS codes according to said masking signal.
 3. The systolic architecture for Comma-Free Reed-Solomon decoding circuit of claim 1, wherein each of said processing element is composed of a first register, a second register, a third register, a combinational circuit (XNOR-AND) and an accumulator; said first register stores the symbols of the CFRS codes beforehand; said second register stores the received code symbols of CFRS codes to facilitate their downward transmission; said third register stores said correlating comparison results; said (XNOR-AND) combinational circuit compares two code symbols in said first register and said second register, respectively, to see whether they are identical; said accumulator adds the comparison result to a final result.
 4. The systolic architecture for Comma-Free Reed-Solomon decoding circuit of claim 1, wherein each of said boundary processing element is composed of a first comparator, a second comparator and a combinational circuit; said first comparator compares the comparison results of the same said row, while said second comparator compares the comparison results of individual rows; said combinational circuit stores the temporary results of said first comparator and those of said second comparator, and sends the comparison result of said row to said second comparator for comparison after said first comparator has made a comparison with respect to said row. 